Bloom Bridge Blog — Triple-B

June 17, 2013 – IMP Odds

The boards last night were pretty quiet, which is just as well, since I am tired from a long tournament, and couldn’t say a lot even if the hands were lively.  I thought I would focus a bit on IMP odds today.  In the KO tactics handout, you were told to bid fairly aggressively for games, bidding vulnerable games with at least a 40% chance, and 50% non-vulnerable games, but to bid more conservatively in the slam zone.  Good advice.  Every wonder why?

Let’s suppose we bid a contract that depends on a finesse, and nothing else.  That makes it a 50-50 bet.  Like any such gamble, we win some and we lose some.  Let’s track the odds.

Case 1:  We bid to a game on a finesse, say four spades, and they stop low at the other table.  If the finesse works, we win.  We will be +420 or +620 against their +170 at the other table.  That translates to a gain of 250 or 450 points.  Converting this to IMPs, we gain 6 IMPs not vulnerable, and 10 IMPs vulnerable.  If the finesse loses, they collect 140, while we pay out 50 or 100.  So, our team loses either 190 points, 5 IMPs, or, vulnerable, 240 points, 6 IMPs. 

Our 50-50 gamble, not vulnerable, stands to win 6 IMPs while risking 5.  So we will end up ahead, by a tiny margin, if we bid every such game.  Vulnerable, we stand to win 10 while risking 6, much better odds, and we want to be in every vulnerable game that needs, essentially, a finesse. 

Case 2:  We bid to six spades, needing a finesse, while they stop in four spades.  Here, not vulnerable, we win 11 IMPs when our finesse works, and lose 11 when it fails.  That is a total toss-up.  Likewise, vulnerable slams are 13 IMP gambles either way. 

Case 3:  We bid to seven spades, on a hook, while they play in six.  When we win, we gain 11 IMPs non-vulnerable, and pay out 14 when the finesse loses.  Here, the 50-50 bet is anti-percentage (as it is vulnerable as well, with a 13 IMP gain risking a 17 IMP loss). 

These are the basic IMP odds.  There are a few weird quirks in the system –

Case 4:  We bid to six diamonds, needing a finesse, while they stop in five.  Again, we gain 11 or 13 IMPs when we win our bet, but surrender either 10 or 12 when we lose.  For some odd reason, minor suit slams are slightly better bets than major suit slams.

The bridge great Zia has said that minor suit slams always seem to make, and we should bid these aggressively.  That’s kind of silly, but he is getting better than a 50-50 return on his gamble.  There is another factor present, and it is very important to understand this principle of IMP strategy:

     Luck on a deal often swings more than a single trick.

What does that mean?  Let’s say we bid to six diamonds, which needs a two-two trump split to make.  Probability tables will tell you that such a split is just a hair over 40%, so this is a poor gamble, and such an overbid should lose over the long haul.  However, some of the time when things go wrong they really go wrong.  Let’s say they bid accurately to five diamonds in the other room, with our side not vulnerable.  40% of the time slam makes and we win 11 IMPs.  Another 40% of the time or so, there are eleven tricks available, and we lose 10 IMPs.  The rest of the time, we can only win ten tricks in diamonds.  We pay out 100, they lose 50 – two IMPs away.  Here’s the math:  In five hands, we win 11 IMPs twice, lose 10 twice, and only two once.  It is a complete wash!

Twice yesterday, in my tournament, this principle came into play.  On the first hand, the auction started,


My opponent overbid to game, while 3H was passed at the other table.  I defended carefully to ensure setting the game, and we went +100.  Good!  Had they stopped in three, I would need to engineer a ruff to set the hand.  That required a riskier defense, but it would have worked.  Had he passed three hearts, we still would have scored 100.  On this layout, his overbid risked zero IMPs! 

On a previous hand, I held a nine count opposite a vulnerable strong notrump.  I blasted into 3NT, and, as the play developed, it became clear that tricks would be hard to establish, so the opponents, two world-class experts stayed passive, and ended up +100.  At the other table, the player in my seat raised to 2NT, and everyone passed.  My teammates could see that declarer would develop an eighth trick in diamonds, so they attacked clubs, hoping for a favorable lie.  The cards cooperated, and they got six in before declarer won eight.  Plus 100, for a push.  My overbid cost us zero IMPs. 

Again, let’s do some really simple math.  Let’s say that one table rests in 3H while the other tries a game.  1/3 of the time game makes, 1/3 it is down one, and 1/3 it goes down two.  Then, if not vulnerable, the wild overbid will score, in three hands,
          +6,   -5,  -2. 
A net loss of 1 IMP in three hands.  Vulnerable:
         +10,   -6,  -3,
a net gain of an IMP. 

This is an odd fact of IMP life.  Aggressive bidding gains when you get lucky, naturally, and loses when you are unlucky.  However, many of the unlucky losses are smaller than expected.  Six diamonds down one is very bad, while six diamonds down two is only a little bad. 

Overtricks are also worth something at IMPs, but an overtrick is typically a single IMP, while the contract is worth much more than that.  Let’s say that you are playing in four hearts, and can take a finesse to make five, but, if the finesse loses, you might go down.  Should you finesse

The answer, NO!  Your goal, on every hand you declare is simple – make your contract.  Your goal on every hand you defend is simple – set the contract.  Don’t worry about the 1 IMP overtricks. 

Again, let’s say that four hearts is not vulnerable, and they are in four hearts, and play safely to take ten tricks at the other table.  If your finesse works, you win one IMP.  If it fails, you lose ten.  Spotting 10-1 odds on a 50-50 play is pretty bad gambling strategy. 

What if the finesse is through the opening bidder, who has to have that card to have enough points to open?  OK, maybe it is worth paying out 10-1 odds on such a finesse, but I still wouldn’t take it, and don’t want you to risk your contracts either. Still, if the danger to the contract is less than 5%, then the finesse is mathematically the correct play, but you will keep your teammates (and me) happy if you simply make all your contracts. 

What if the contract is some partscore?   I will sometimes risk a 1NT contract for an overtrick, knowing that I might lose 4 or 5 IMPs when I am wrong, if I figure the try is a big favorite.  Again, this is correct IMP odds management, but I would still like you to work on guaranteeing your contracts. 

This brings me to the one hand from yesterday worth griping about:



South played in four hearts on this (slightly optimistic) auction:

All Pass


In general, a jump to three hearts suggests a hand worth around a strong notrump in support of hearts.  A hand like



is a clear three heart call, and that’s about what I would expect for a three heart call, not a balanced 12-14 point hand with four hearts.  I admit that the North hand has improved on the auction, so I consider 3H just a mild overbid. 

To the play:  West led the club five.  North played low, and South took East’s nine with the ten.  A lead in dummy’s first suit is a bit suspicious, so this lead could well be a singleton, and the defense might score a club ruff.  Let’s count our tricks:


  1.  We have one spade and two diamonds.
  2. We have four club winners, though one of them might get trumped away.
  3. Once we knock out the trump ace, we have three heart winners.
  4.  We can trump a diamond in hand quickly, or a spade in dummy eventually.

That seems like eleven winners.  Even if someone trumps a club, we should come to ten.  Perfect.  So it looks right to start on trumps next, before too many of our good clubs get trumped.  Declarer correctly played a trump to the queen and a trump back to the king.  On the second trump, East discarded the diamond two, and West withheld the ace.  What now?

Four-one trumps is unfortunate, but, even if the lead was a singleton, East can’t get in to deliver a ruff, so ten tricks look easy.  We could simply continue trumps and take our ten winners.  If you looked no further, fine!  The goal is to make your contract.  There are, in fact, safe ways to try for 11 tricks, but South, at the table, simply led another trump, and I heartily approve. 

West won this trump.  Let’s consider two cases now.  Suppose West plays another trump, clearing all the trumps from both hands.  We have ten sure tricks.  Can we try, safely, for an overtrick?

Yes, we could try a diamond finesse.  Even if it loses, we still have stoppers, the spade ace and the diamond king, and so will get in to cash our winners.  This is a perfectly safe attempt at an overtrick.

The second case occurred at the table.  West shifted to a low spade, and East put up the queen.  If there a safe way to try for eleven tricks now?

Yes.  We can win and play diamond ace, diamond king, diamond ruff.  Then we try to get to dummy to draw the last trump.  If West ruffs the club, or any diamond, we still make four. 

There seem to be two other ways to try for an extra trick:

  1.   We could duck this spade, and try to trump a spade in dummy, or
  2. We could try a diamond finesse. 

Both of these tries are poor.  Why?

Ruffing a spade in dummy risks nothing, but gains nothing.  Once we trump a trick in dummy, West’s nine of hearts is high, and we can’t make eleven tricks. 

The diamond finesse might gain a trick, but, if it loses and West can trump a club, we have gone down in our game.  That’s the big no-no.  In fact, if it loses, and the defense continues spades, West will win the setting trick with the heart nine. 

At the table, declarer tried a diamond finesse, giving out those 10-1 odds on a finesse.  The finesse won, so the gamble earned an IMP.  Lucky?  Yes.  But not skillful. 

New rule:

     Don’t try for an overtrick unless you are absolutely sure the contract won’t be jeopardized.  Once you are sure, check again to be really, really sure!

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